text large_stringlengths 384 2.05k | rank_avg float64 1 4.19k ⌀ | rank_max float64 1 8.21k ⌀ | rank_min float64 1 5.03k ⌀ | rank_median float64 1 4.21k ⌀ | rank_by_avgsim float64 1 4.19k ⌀ | avgsim_to_github float32 0.77 0.85 ⌀ | dataset large_stringclasses 1
value |
|---|---|---|---|---|---|---|---|
d in is given by $$\begin{cases}
{\mathbb Z}^{abc} &\rightarrow {\mathbb Z}^a \oplus {\mathbb Z}^b \oplus {\mathbb Z}^c \\
(x_{l,m,n}) &\mapsto \Big( \sum_{m,n} x_{l,m,n}, \sum_{l,n} x_{l,m,n}, \sum_{l,m} x_{l,m,n} \Big).
\end{cases}$$ We conclude that the multiplicity of a weight $\delta = (\delta^A, \delt... | 1,001 | 1,330 | 1,425 | 896 | null | null | github_plus_top10pct_by_avg |
Thank you for any help you can give.
A:
Please Please Please do not do this.
Make every date a new row.
Make a date column.
So your table would look something like this:
ID | Date | Attendance |
1 | 2011-11-01 | 5 |
2 | 2011-11-02 | 12 |
3 | 2011-11-03 | 3 ... | 1,002 | 6,566 | 78 | 488 | 2,061 | 0.783117 | github_plus_top10pct_by_avg |
s of the restriction of the given immersion $f$ ($g$) to the submanifold in $M^{n-1}$ ($N^{n-2}$) dual to $w_1(\kappa)^{k-1} \in H^{k-1}(M^{n-1};\Z/2)$ ($w_2(\eta)^{k-1} \in H^{2k-2}(N^{n-2};\Z/2)$).
Let $(g,\Xi,\eta)$ be a $\D_4$-framed (generic) immersion in the codimension $2k$. Let $h: L^{n-4k} \looparrowright \R^... | 1,003 | 1,515 | 954 | 927 | null | null | github_plus_top10pct_by_avg |
ely dotted](0,.13-1.5*.125)--++(0,1.5*.25);\end{tikzpicture}}},;\star),\qquad
\gyoung(;1;2;3_{1.5}{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(1.5*.25,0);\end{tikzpicture}}};v;\star_{1.5}{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(1.5*.25,0);\end{tikzpicture}}}... | 1,004 | 606 | 1,313 | 1,093 | 206 | 0.818426 | github_plus_top10pct_by_avg |
\]) can be written in compact form as $$\begin{aligned}
\frac{\partial\mbox{\boldmath$\zeta$}}{\partial t}
&=&-\frac{i}{\hbar}
\left[
\begin{array}{cc}\frac{\partial{\cal H}}{\partial\vert\psi\rangle}
&\frac{\partial{\cal H}}{\partial\langle\psi\vert}
\end{array}
\right]
\cdot\mbox{\boldmath$\Omega$}\cdot
\left[\begin{... | 1,005 | 274 | 1,214 | 1,068 | null | null | github_plus_top10pct_by_avg |
ficient algorithms tailored for independent paired comparisons. However, due to the ignored dependencies in the data, naive rank-breaking approaches can result in inconsistent estimates. The key idea to produce accurate and consistent estimates is to treat the pairwise comparisons unequally, depending on the topology o... | 1,006 | 774 | 353 | 696 | null | null | github_plus_top10pct_by_avg |
} - q^{\frac{2-r+1}2}\right)$$ which combined with Theorem \[euler-spec\] gives $$\label{expansion-combo}
\H_{(n-1,1)} \left(\sqrt{q},\frac1{\sqrt{q}}\right)
= \sum_{\substack{rs=2n\\ r\not\equiv s\mod2}}
(-1)^r \left( q^{\frac{s-r-1}2} - q^{\frac{2-r+1}2}\right)$$
We compute the logarithm of the left hand side of a... | 1,007 | 1,864 | 1,143 | 1,054 | 2,580 | 0.778714 | github_plus_top10pct_by_avg |
inite constant. It follows that rank-breaking requires the effective sample size $n\ell=O(d\log d / \varepsilon^2 )$ in order to achieve arbitrarily small error of $\varepsilon>0$, on the weakest $\ld=\ell\,d/(2 \kappa)$ items.
Real-World Data Sets {#sec:real}
====================
On real-world data sets on sushi pre... | 1,008 | 901 | 196 | 901 | 355 | 0.812303 | github_plus_top10pct_by_avg |
re crank form expressions as they are, by induction on the lengths of the words in the alphabets ${\cal L}_n$, any word turn out to be equal to (a scalar multiple) of the standard expression of a seat-plan $w$ of $\Sigma_n^1$. Hence we have $$\mbox{rank}\ \widetilde{A_{n}(Q)} \leq |\Sigma_n^1|.$$
As Tanabe showed in [... | 1,009 | 325 | 969 | 1,020 | 2,445 | 0.779686 | github_plus_top10pct_by_avg |
Unit N[^a^](#t001fn001){ref-type="table-fn"} Median (Range) Lower limit (90% CI) Upper limit (90% CI)
---------------------------------------------------- --------------- ----------------------------------------- --------------------------- ---------------------- --------... | 1,010 | 4,967 | 605 | 754 | null | null | github_plus_top10pct_by_avg |
|\cR(2,4)|>1$\
By \[prop:qij\] this implies that $\cR(3,5)=\emptyset$ and, hence, for $i\in\{2,4\}$, that $\sum_{k\in C_{i}}|\cR(i,k)|\ge|\cR\setminus\cR^*|-1$. Using equation (\[eq:individual\]) we get that $\sum_{k\in C_2}|\cR(2,k)|+|\cR^*|+2+|\cS_2^*|\le 4+|\cS^*|$. Since $7+|\cS_2^*|\le|\cR|+1+|\cS^*_2|... | 1,011 | 315 | 434 | 1,128 | null | null | github_plus_top10pct_by_avg |
our study were spaced plants so it was not possible to calculate yields in t ha^−1^ from the values of individuals. However, in a study comparing 15 diverse genotypes harvested in autumn (September--October), a maximum yield of 19 t ha^−1^ was reported (Clifton‐Brown *et al*., [2001](#gcbb12419-bib-0009){ref-type="ref... | 1,012 | 631 | 1,634 | 1,277 | null | null | github_plus_top10pct_by_avg |
o$ is the initial distribution $Y_0$, then we have that $||\rho||_\pi{\leqslant}{\mathcal{O}}(n^{\delta})$. Applying Theorem \[chernof\] implies that $${\ensuremath{\operatorname{\mathbf{Pr}}\left[\sum_{t=1}^{n}f(Y_t){\geqslant}\mu \cdot n\right]}}
={\mathcal{O}}(n^{\delta}){\mathrm{e}}^{-\Theta(rn^{1-3\delta})}=n^{-... | 1,013 | 420 | 799 | 1,031 | 1,408 | 0.789952 | github_plus_top10pct_by_avg |
nu_j\gamma^j$. Since $\mu \mod p_i \ne 0$, there exists $j$ such that $\mu_j \mod p_i \ne 0$. So $(a_\tau\mod p_i)=(\mu_j \mod p_i)^{-1}(\nu_{j+{\langle \bu_\tau,\bz \rangle}} \mod p_i)$. So we can find $a_\tau \mod p_i$ for each $i\in[r]$. Finally we use Chinese Remainder Theorem to find $a_\tau \in \Z_m$.
Proof of L... | 1,014 | 941 | 1,077 | 921 | null | null | github_plus_top10pct_by_avg |
rectangular. As we observed above $\delta(\muhat)\geq (2g-2)n$. Hence if $\delta(\muhat)=0$ then $g=1$ or $g=0$. If $g=1$ then necessarily $\mu^i=(n)$ and $\Gamma$ is the Jordan quiver $J$.
If $g=0$ then $\delta=0$ is equivalent to the equation $$\label{affine-eqn}
\sum_{i=1}^k\frac{1}{l_i}=k-2,$$ where $l_i:=n/t_i$ ... | 1,015 | 794 | 1,017 | 993 | null | null | github_plus_top10pct_by_avg |
guarantees:
[https://github.com/dhall-lang/dhall-lang/wiki/Safety-
guarant...](https://github.com/dhall-lang/dhall-lang/wiki/Safety-guarantees)
The main risks in executing potentially malicious Dhall code that is not
protected by a semantic integrity check are:
* Using more computer resources than you expected (i.e.... | 1,016 | 68 | 529 | 1,022 | 689 | 0.80232 | github_plus_top10pct_by_avg |
frac{i m \left(u^2-1\right)}{u^2+1} & 0 & -\frac{i m \left(u^4+6 u^2-3\right)}{4 \left(u^2+1\right)} \\
\mathcal{D}_{Ru} & 0 & \frac{i m}{2 \left(u^2+1\right)} & 0 & -\frac{i m \left(u^4+6 u^2-3\right)}{8 \left(u^4-1\right)} & 0 \\
\mathcal{D}_{uu} & 0 & 0 & 0 & 0 & 0 \\
\mathcal{D}_{TR} & 0 & -\frac{u \left(u^2-3\r... | 1,017 | 905 | 1,247 | 1,078 | null | null | github_plus_top10pct_by_avg |
}_{{\widehat{S}}} = \bigotimes_{j \in {\widehat{S}}}^n E_j.$$ Then, a standard result about confidence sets for medians along with union bound implies that $\hat{E}_{{\widehat{S}}}$ is a $1-\alpha$ confidence set for the median LOCO parameters, uniformly over $\mathcal{P}_n$.
For every $n$, $$\inf_{w_n \in \mathcal{W}... | 1,018 | 2,264 | 965 | 1,072 | null | null | github_plus_top10pct_by_avg |
uiv& E_2-E_1
\nonumber\\
&=&p\frac W2 \frac{1-x_-^2}{1+x_-^2-x_-^{2\gamma}}x_-^{2\gamma}
\left(x_--x_-^{-1}\right) \; ,\end{aligned}$$ or $$\label{eq:relative}
\frac{\Delta E}{E_0} = -\frac{\left(1-x_-^2\right)^2x_-^{2\gamma-1}}
{\left(1+x_-^2-x_-^{2\gamma}\right) \sqrt{\frac{4\nu^2}{W^2}+1}}\;.$$
As with... | 1,019 | 4,529 | 446 | 853 | 1,324 | 0.791016 | github_plus_top10pct_by_avg |
we expand the exponential and Laguerre in Eq. (\[auxf1\]) up to second order in $\eta$ to find $$\begin{aligned}
\label{fauxap}
\left|{f_n^m}\right|^{2} &\approx& \frac{(n+m)!}{n!m!^2}
\left[1 - \frac{2n+m+1}{m+1} \eta^2 \right]{\eta^{2m}}. ... | 1,020 | 1,559 | 1,162 | 1,101 | null | null | github_plus_top10pct_by_avg |
events reading from or clearing the output buffers of the partition $j$. For any memory area $a$ of the system ($\mathcal{M}$), $a$ is a memory area in the partition $j$ ($A_j$), if the value of $a$ in state $s$ and $s'$ are not equal.
The No-Infiltration Property states that data processing in a partition is not inf... | 1,021 | 2,832 | 1,862 | 1,134 | 520 | 0.807139 | github_plus_top10pct_by_avg |
45 (4) 0.78542 (19) 0.0251 (11)
H66 1.0388 0.3787 0.8055 0.030\*
C67 0.9514 (3) 0.3723 (4) 0.80778 (19) 0.0286 (12)
H67 0.9612 0.3739 0.8434 0.034\*
C68 0.8912 (3) 0.3677 (... | 1,022 | 4,519 | 313 | 614 | null | null | github_plus_top10pct_by_avg |
^\chi ({\alpha },\beta _\nu ;t)$ for all $\chi \in {\overline{{\mathcal{X}}}}_3$, ${\alpha }\in {\mathbb{N}}_0^I$, $\beta _\nu \in R^\chi _+$, and $t\in
{\mathbb{N}}$ with $t<{b^{\chi}} (\beta _\nu )$ by $$\begin{aligned}
{P}^\chi ({\alpha },\beta _\nu ;t)=\Big|\Big\{(m_1,\dots ,m_n)\in {\mathbb{N}}_0^n\,\big|\,
\s... | 1,023 | 1,312 | 810 | 1,011 | null | null | github_plus_top10pct_by_avg |
rent from $S$. If $i>2$ then we apply Lemma \ref{lemma7} to move the $2$ from row $3$ to row $2$; neglecting the tableau not dominated by $S$ and (in the case $j>2$) neglecting the tableau with two rows equal to $\young(j)$, the only tableau we get is}}
U''[i,j]&={\text{\footnotesize$\gyoungx(1.2,;1;1;2;{{\begin{tikzpi... | 1,024 | 1,679 | 843 | 995 | 921 | 0.797596 | github_plus_top10pct_by_avg |
g(a, c'), \end{aligned}$$ where $c' := \lvert c / b \rvert^{\frac{1}{a}}$. Therefore, for any $c \in \mathbb{R}$, we have $$\begin{aligned}
\label{E[Pe(Z+c)]-2}
\operatorname{{E}}[\Pe(Z + c)]
= \frac{(k_{1} - k_{2}) c}{2}
+ \frac{(k_{1} + k_{2}) \lvert c \rvert}{2 \G(a)}
\g\left(a, \left\lvert \frac{c}{b} \right\rve... | 1,025 | 2,068 | 1,294 | 1,023 | null | null | github_plus_top10pct_by_avg |
-1}\left( |\cos\Theta_{0}|g\epsilon^{\prime \prime} \right)\right]} }{4 \left( e^{\frac{2 \pi \omega}{g}}-1\right)}
\notag
\\[1ex]
& \hspace{13ex}
\times \frac{\sin \left( \frac{\omega}{g} \cosh^{-1} (c) \right)}{\sqrt{1-{c^{\prime}}^2} \sqrt{1-{c^{\prime \prime}}^2} \sinh \left[ \cosh^{-1} (c) \right] } \; \; \b... | 1,026 | 3,431 | 1,141 | 1,122 | null | null | github_plus_top10pct_by_avg |
}{m_\pi(W;v)}-\frac{\Vert\nabla_W m_\pi(W;v)\Vert^2]}{\{m_\pi(W;v)\}^2}\bigg].\end{aligned}$$ Combining this identity and Lemma \[lem:identity\] completes the proof. $\Box$
Using Lemma \[lem:identity2\] immediately establishes the following proposition.
\[prp:cond\_mini\] $\ph_\pi(Y|X)$ is minimax relative to the KL ... | 1,027 | 1,031 | 1,635 | 1,044 | 3,833 | 0.769791 | github_plus_top10pct_by_avg |
$ for all $i,j\in I$. Choose the ideal $J$ in Lemma \[le:Uzideal\] as explained above. Then one gets the Shapovalov determinants of $U_q({\mathfrak{g}})$ and $u_q({\mathfrak{g}})$ from the one of $U(\chi )$ in Thm. \[th:Shapdet2\].
The second part of Thm. \[th:ShapdetUqg\] was proved in [@a-KumLetz97] in the case when... | 1,028 | 525 | 1,086 | 1,095 | 3,966 | 0.768923 | github_plus_top10pct_by_avg |
A/C versus C/C genotype, we calculated an increased crude OR of 2.67 (95% CI = 1.26, 5.65; *P* = 0.0089) for RVR (+) versus RVR (−). The association of rs12126768 genotypes with RVR remained significant in the HCV-2 infected group (*P* = 0.0436). Therefore, HCV infected individuals with the *GNB1* rs4648727 C/C and rs1... | 1,029 | 3,142 | 1,179 | 1,030 | null | null | github_plus_top10pct_by_avg |
}^{m_n}=0
\label{eq:lindep}
\end{aligned}$$ in $U^+(\chi )$. Let ${T}^-={T}^-_{i_\mu }\cdots {T}^-_{i_2}{T}^-_{i_1}$. Since ${T}^-(E_{\beta _\mu })={T}^-_{i_\mu }(E_{i_\mu })
=K_{i_\mu }^{-1}F_{i_\mu }$, we obtain that $$\sum _{m_\mu ,\dots ,m_n}
a _{m_\mu ,\dots ,m_n}
(K_{i_\mu }^{-1}F_{i_\mu })^{m_\mu }{T... | 1,030 | 1,775 | 1,508 | 1,015 | null | null | github_plus_top10pct_by_avg |
`gi 87161394 ref` `71` `KKVLLTGLGIVI`
... | 1,031 | 6,114 | 356 | 252 | null | null | github_plus_top10pct_by_avg |
above $1$), for very gently inclined straight lines. On the other hand, a steeper straight line indicates a faster reduction of layer sizes as we progressively move toward layer $0$ from layer $K-1$ through the other layers. In the analysis that follows, then, we also use the slope of the least-squares linear approxim... | 1,032 | 2,103 | 3,011 | 1,159 | null | null | github_plus_top10pct_by_avg |
, S., [Hosokawa]{}, T., [Yoshida]{}, N., [Omukai]{}, K., & [Yorke]{}, H. W. 2015, , 448, 568
, D., [Johnstone]{}, D., [Lizano]{}, S., & [Shu]{}, F. 1994, , 428, 654
, T., [Hirano]{}, S., [Kuiper]{}, R., [et al.]{} 2016, , 824, 119
, T., [Omukai]{}, K., [Yoshida]{}, N., & [Yorke]{}, H. W. 2011, Science, 334, 1250
,... | 1,033 | 1,236 | 3,085 | 1,217 | null | null | github_plus_top10pct_by_avg |
{\pmb{\sum}}}}$(sequential)**
Let $X$ be a compact sequential space. Let $Y\subseteq X$, $|Y|=\aleph_1$. Suppose $\{W_\alpha\}_{\alpha\in\omega_1}$, $\{V_\alpha\}_{\alpha\in\omega_1}$ are open subsets of $X$ such that:
- $W_\alpha\subseteq\overline{W_\alpha}\subseteq V_\alpha,$
- $|V_\alpha\cap Y|\leq\aleph_0$,
... | 1,034 | 2,071 | 1,865 | 1,053 | 2,929 | 0.776008 | github_plus_top10pct_by_avg |
ons).
Before closing, we would like to emphasize that the proposed shear-based parameterizations are only applicable away from the surface. Near the surface, due to the blocking effect [see @hunt88; @hunt89], $L_C$ or $L_H$ cannot be a representative length scale. They should be properly combined with an explicit para... | 1,035 | 107 | 1,847 | 1,001 | 1,661 | 0.787091 | github_plus_top10pct_by_avg |
$L_j$ is free of type $I$}.
\end{array}\right.$$ We emphasize that we have $2z_j^{\ast}$, not $\pi z_j$, when $j$ is even.
In Lemma \[la9\], we will show that $F_j$ is isomorphic to $ \mathbb{A}^{1} \times \mathbb{Z}/2\mathbb{Z}$ as a $\kappa$-variety so that it has exactly two connected components, by enumerating equ... | 1,036 | 465 | 542 | 1,168 | 2,291 | 0.78113 | github_plus_top10pct_by_avg |
ls with $u=1, \ldots, {u_{\max}}$ MUs, for some maximum size ${u_{\max}}$. The paper proceeds as follows. Section \[sec:Model\] presents the neuromuscular model of @Rid06 for a fixed number of MUs and defines the priors for the model parameters. Section \[sec:Method\] describes the SMC-MUNE method. Due the complexity o... | 1,037 | 151 | 1,016 | 924 | 2,978 | 0.775647 | github_plus_top10pct_by_avg |
\Delta_{m+n+1}+\Delta_{m-n+1}+\Delta_{m+n-1}+\Delta_{m-n-1})\big]
\eqno(A4)$$
$$\bigg < \bar{K}^+ \bar{\nu} \bigg | -{\tau_0^2 \alpha^2 \over 4}
F^2\bigg | K^+ \nu \bigg
> =- {\pi \tau_0^2 \alpha^2 \over 4}\sum_{m=0}^{\bar{K}}\sum_{n=0}^{K}
c_{\bar{K}m} c_{Kn} \Delta_{\bar{\nu}-\nu}$$ $$\big[ P_1 \Delta_{m-n}+{1\ove... | 1,038 | 2,520 | 776 | 1,007 | null | null | github_plus_top10pct_by_avg |
ot{y}}}_{m}}}{2} \right)}^{2}}+{{\left( \frac{mg}{2} \right)}^{2}}}+m{{\ddot{x}}_{m}}.
\end{array}$$ Nonetheless, if ${{\ddot{x}}_{m(t)}}<0$, those forces can be obtained by $$\label{eq10}
\begin{array}{r@{}l@{\qquad}l}
{{F}_{1}}&=\frac{1}{\mu }\sqrt{{{\left( \frac{m{{{\ddot{y}}}_{m}}}{2} \right)}^{2}}+{{\l... | 1,039 | 4,262 | 332 | 848 | null | null | github_plus_top10pct_by_avg |
*Social Pressure*
my friends drink 0.61
it is difficult to refuse 0.46
other people are drinking 0.77
it will enhance my creative ability 0.51
it is customary for men on s... | 1,040 | 5,784 | 521 | 334 | null | null | github_plus_top10pct_by_avg |
to $k=1$ as in the argument below Claim \[claim2\], we obtain the theorem.
To prove Claim \[claim3\], let $\eta_1,\dots, \eta_n$ be an independent sequence of random variables distributed as $\eta_i\sim N(0, \frac{\overline{\sigma}_i^2}{\overline{B}_n^2})$ and be independent of $\{X_1, \dots, X_n\}$, and let As in [4]... | 1,041 | 388 | 237 | 1,161 | 3,575 | 0.771461 | github_plus_top10pct_by_avg |
re not possible. Proverbially, the forest may be secure but each of the trees reveals enough information to reconstruct the possible forests. By eliminating approximately one quarter of the key options from each qubit we see that by measuring all the individual qubits in a random basis does in fact reveal a great deal ... | 1,042 | 114 | 1,778 | 1,002 | null | null | github_plus_top10pct_by_avg |
-
We highlight the fact that the limiting SDE of a discrete process, $$\label{e:disc-mcmc-new}
w_{k+1} = w_k - s\nabla U(w_k) + \sqrt{s} \xi(w_k, \eta_k),$$ depends only on the covariance matrix of $\xi$. More specifically, as long as $\xi$ satisfies $\sqrt{\E{\xi(w, \eta)\xi(w, \eta)^T}} = M(w)$, will have as its... | 1,043 | 741 | 950 | 984 | 1,470 | 0.789165 | github_plus_top10pct_by_avg |
in terms of $\varphi$ rather than in $A_0$, and $g_k^2=g^2/Z_0$ is nothing but the running coupling at momentum $\vec p^2\sim k_{\rm phys}^2$. Thus we estimate $g_k^2=4\pi \alpha_s(\vec p^2=k_{\rm phys}^2)$. Note that $g_k$ is an RG-invariant. The momentum integration can be performed analytically, and we are led to $$... | 1,044 | 2,170 | 1,537 | 1,064 | 1,455 | 0.789344 | github_plus_top10pct_by_avg |
a_{n}$ with other numbers $n$ into the second expression (\[eq.3.1.4\]) for the potential $V_{2}(r)$, one can construct the whole hierarchy of the radial reflectionless potentials of this new type.
In Fig. \[fig.1\] the potential $V_{2}(r)$ for the chosen values of the parameters $C$ and $\gamma_{n}$ is shown. From he... | 1,045 | 334 | 439 | 1,254 | 1,719 | 0.786458 | github_plus_top10pct_by_avg |
b}-1}{q}
\prod _{t=1}^{{b}-1}(q^{t+1-{b}}\Lambda (K_p)-\Lambda (L_p))v_\Lambda
\end{aligned}$$ by Lemma \[le:EmFn\]. By assumption, ${\hat{T}}'(v_\Lambda )\not=0$, and hence ${\hat{T}}'$ is a nonzero multiple of ${\operatorname{id}}_{M^\chi (\Lambda )}$. Therefore ${\hat{T}}_p$ is an isomorphism. The proof for ${... | 1,046 | 893 | 666 | 1,006 | null | null | github_plus_top10pct_by_avg |
this result:
[memtest]$ g++ -O2 mem.cpp -o mem
[memtest]$ ./mem
size start prev.size
-----------------------------------
BLOCK 0: 08b, 0x1f47030
BLOCK 1: 08b, 0x1f47050, 32b
BLOCK 2: 16b, 0x1f47070, 32b
BLOCK 3: 16b, 0x1f47090, 32b
BLOCK 4: 04b, 0x1f470b0, 32b
BLOCK 5: 04b, 0x1f470d0, 32b
BL... | 1,047 | 1,207 | 581 | 965 | null | null | github_plus_top10pct_by_avg |
------------------ ------------------
**WMC**
OSPANs 14.656 (5.036) 14.938 (5.147) 24.719 (11.312) 19.969 (9.177) ... | 1,048 | 1,620 | 1,269 | 1,231 | null | null | github_plus_top10pct_by_avg |
eudonatural transformation, giving a 2-category . We can define two-variable morphisms of left derivators, and (separate) preservation of colimits, just as for derivators.
A **monoidal left derivator** is a left derivator with a pseudo-monoid structure that preserves colimits separately in both variables. If is a mono... | 1,049 | 1,214 | 1,444 | 1,021 | 2,335 | 0.780784 | github_plus_top10pct_by_avg |
\pm$5.0 27.5$\pm$2.0 5.7$\pm$0.1
1b 05 39 52.10 -69 45 23.17 36 28.1$\pm$2.8 170.3$\pm$17.0 231.8$\pm$11.6 152.4$\pm$7.6 57.7$\pm$4.1 23.9$\pm$1.7 9.1$\pm$0.6 1.6$\pm$0.1
1c (N159W) 05 39 32.51 -69 46 02.74 68 48.7$\pm$4.9 481.2$\... | 1,050 | 3,467 | 248 | 808 | null | null | github_plus_top10pct_by_avg |
motion for the wave fields can be written in compact form as $$\frac{\partial\mbox{\boldmath$\zeta$}}{\partial t}=\frac{i}{\hbar}
\{ {\cal H}[\mbox{\boldmath$\zeta$}] , \mbox{\boldmath$\zeta$} \}_{\mbox{\tiny\boldmath$\cal B$}} \;.
\label{eq:wein_eqofm}$$ The compact form of Eq. (\[eq:wein\_eqofm\]) can be set into an... | 1,051 | 381 | 1,580 | 1,194 | 3,842 | 0.769745 | github_plus_top10pct_by_avg |
suitable and short tree iterable $a$-premouse", then there could be $\Q\in \mathcal{F}(\b, a, \P)$ which is not in $\mathcal{F}(\a, a, \P)$. However, we always have the following easy lemma.
\[inclusion\] Suppose $\a<\b<\k$ are two ordinals which end weak gaps and such that $J_\a(\mathbb{R})$ and $J_\b(\mathbb{R})$ bo... | 1,052 | 1,911 | 1,210 | 992 | null | null | github_plus_top10pct_by_avg |
alculation by induction on $n$.
An analogue of Lusztig’s PBW basis {#sec:Lusztig}
==================================
Let $\chi \in {\mathcal{X}}$ and $p\in I$. Assume that $\chi $ is $p$-finite. Let $q_{i j}=\chi ({\alpha }_i,{\alpha }_j)$ and $c_{p i}=c_{p i}^\chi $ for all $i,j\in I$.
For all $m\in {\mathbb{N}}_0$... | 1,053 | 1,705 | 1,230 | 1,076 | null | null | github_plus_top10pct_by_avg |
\delta_{i-1}v_{i-1}\cdot {}^tm_{i, i-1}^{\prime}+\delta_{i+1}v_{i+1}\cdot {}^tm_{i, i+1}^{\prime} =0
~~~ \left(=\pi (m_{i,i}^{\ast\ast})^{\prime}\right).\\
\end{array}
\right.$$
Here, notations follow from those of (e) and (f) in the description of an element of $\tilde{M}(R)$.
Here, all ma... | 1,054 | 788 | 1,070 | 1,056 | 2,413 | 0.779988 | github_plus_top10pct_by_avg |
fore achieved by storing a single grid of values for each unique firing pattern to date.
A higher-order Newton-Cotes numerical integration method would produce a more accurate estimate of , but the associated interpolated density surface of piecewise polynomials would not be guaranteed to be bounded below by zero, mak... | 1,055 | 453 | 1,696 | 1,142 | 1,943 | 0.784243 | github_plus_top10pct_by_avg |
independent quantities $\one$, $\gamma_5$, $\gamma^\mu$, $\gamma^\mu\gamma_5$ and $\sigma^{\mu\nu}$ (one has indeed $\sigma^{\mu\nu}\gamma_5=i\epsilon^{\mu\nu\rho\sigma}\sigma_{\rho\sigma}/2$ where $\epsilon^{0123}=+1$).
Further identities involving four Dirac spinors are also important to establish supersymmetry inva... | 1,056 | 210 | 893 | 1,092 | null | null | github_plus_top10pct_by_avg |
in .
\[cor:accuracy.beta\] With probability at least $ 1- \frac{2}{n}$, the maximal length of the sides of the hyper-rectangle $\tilde{C}_{{\widehat{S}}}$ is bounded by $$C \sqrt{ \frac{\log k}{n} \left( \frac{k^{5/2}}{u_n^3 u^2} \overline{v} \sqrt{ \frac{\log n}{n}} + \frac{k }{u^4} \overline{v}\right) },$$ for a ... | 1,057 | 244 | 798 | 1,193 | 3,177 | 0.774268 | github_plus_top10pct_by_avg |
{\prime}}^{\iota *}(X,t)
\chi_{\alpha^{\prime}\alpha}(X)\;,
\label{eq:qc-ave-ad}$$ where the coefficients $C_{\alpha}^{\iota}(X,t)$ and $C_{\alpha^{\prime}}^{\iota *}(X,t)$ are evolved according to Eqs. (\[eq:c\]) and (\[eq:cstar\]), respectively. Equations (\[eq:c\]) and (\[eq:cstar\]) are non-linear equations which c... | 1,058 | 4,506 | 1,835 | 1,107 | null | null | github_plus_top10pct_by_avg |
's suppose to give back the assets in order based on t.Count but I think it might not be working because the .Count is actually not part of asset which is what is being selected, but I have no idea how to fix this.
As you can see there is an assetVisits table and an assets table, and I need to get back the assets in or... | 1,059 | 997 | 190 | 315 | null | null | github_plus_top10pct_by_avg |
mogorov--Smirnov test, the residual gutta-percha and sealer data were not normally distributed. Therefore, a nonparametric Kruskal--Wallis and post hoc Dunn's tests were used, at P=0.05 to compare the mean area of residual gutta-percha and sealer. All the statistical analysis were performed with SPSS 21.0 (IBM Corp., A... | 1,060 | 61 | 1,242 | 1,376 | null | null | github_plus_top10pct_by_avg |
e the representative galaxy for the observed universe. This representative galaxy could, in principal, be found by sectioning the observed universe into three-dimensional, non-overlapping cells of different sizes centered on each galaxy. By surveying these cells, a representative galaxy, with an average $v_H^{*}$ and $... | 1,061 | 4,048 | 1,622 | 858 | 2,239 | 0.781501 | github_plus_top10pct_by_avg |
GC simultaneously, that's why your require -XX:+UseParNewGC to be paired with CMS otherwise use -XX:+UseSerialGC explicitly OR -XX:-UseParNewGC if you wish to use serial method against young generation
A:
UseParNewGC usually knowns as "parallel young generation collector" is same in all ways as the parallel garbage c... | 1,062 | 4,695 | 641 | 915 | 1,627 | 0.787422 | github_plus_top10pct_by_avg |
F(t)\Psi\
=&\ \frac{1}{1+\Xi(D_\eta(t)-\eta)}\,\Psi
\nonumber\\
=&\ \Psi + \Xi[\![A_\eta(t)\,, \Psi]\!]
+ \Xi[\![A_\eta(t),\Xi[\![A_\eta(t), \Psi]\!] ]\!]+\cdots\,.
\label{def F}\end{aligned}$$ The map $F(t)$ has a property that changes $D_\eta(t)$ into $\eta$: $$D_\eta(t)F(t)\ =\ F(t)\eta\,.
\label{important proper... | 1,063 | 1,469 | 1,119 | 1,029 | null | null | github_plus_top10pct_by_avg |
ections \[sec:cart\_int\] and \[s:interior\_solver\_cylindrical\] below, $\rho_{i,j,k}$ is any arbitrary density distribution on the grid, and in fact represents a different quantity for each of the three instances where we solve for the interior potential.
Cartesian Grid Solution with Zero Boundary Value {#sec:cart_i... | 1,064 | 2,992 | 1,322 | 1,052 | null | null | github_plus_top10pct_by_avg |
the appendix. We quote the final, exact form here [@Pierce:1996zz].
m\_b\^ = \[Eq:fullgluino\] ,
where the momentum of the bottom quark is given by $p$. In the limit $p \rightarrow 0$ (which is a good assumption here since $p^2 = m_b^2$), the Passarino-Veltman functions can be written as B\_0(0, , m\_) &=& - () + 1 +... | 1,065 | 127 | 1,965 | 1,154 | 3,050 | 0.7752 | github_plus_top10pct_by_avg |
y Theorem \[210\], there is a suitable basis for this lattice such that the norm of the $\pi^1$-modular Jordan component is the ideal $(4)$. Namely, we choose $$(e_5-e_1', e_1'-\frac{2\pi(b+b') }{\delta(1+4b')}e_2', \pi e_5+\frac{a}{1+4b'}e_2').$$ Here, a method to find the above basis follows from the argument used in... | 1,066 | 2,050 | 1,342 | 1,024 | 3,220 | 0.773925 | github_plus_top10pct_by_avg |
e show that has the same distribution as $x_t$ in , and has the same distribution as $y_t$ in . Thus, for any $t$, the process $(x_t,y_t)$ defined by is a valid coupling for and .
[One step contraction]{} \[ss:step\_gaussian\]
\[l:gaussian\_contraction\] Let $f$ be as defined in Lemma \[l:fproperties\] with parameter... | 1,067 | 1,987 | 876 | 1,037 | null | null | github_plus_top10pct_by_avg |
rac{1}{\kappa-1} + \cdots + \frac{1}{\kappa-b+1}\bigg) \Bigg) \,, \label{eq:crC3}\end{aligned}$$ such that, $$\begin{aligned}
\label{eq:cr10}
\frac{\partial^2\P(\theta)}{\partial\theta_i^2}\bigg|_{\theta = {\boldsymbol{0}}} &=& \I_{\{ \Omega^{-1}(i) > p \}}A_1\Big((-A_2)(-A_2) - C_1 \Big) + \I_{\{ \Omega^{-1}(i) = p \... | 1,068 | 691 | 1,248 | 1,061 | 3,697 | 0.770612 | github_plus_top10pct_by_avg |
of $X$’s is : :j\^r: = f\^[-r]{} :X\^[r]{}: + (:X\^[r+1]{}:). So to get the order of the coefficient that multiplies and operator $:j^r:$, it is enough to look for the coefficient of the terms multiplying $f^{-r}:X^r:$ in the OPE . These terms have a coefficient of order: f\^[-2p-2+n+m+p+1+|n+1-m-p|]{}={
[lll]{} f\^[... | 1,069 | 290 | 1,563 | 1,191 | 2,644 | 0.778195 | github_plus_top10pct_by_avg |
a i\delta} \lrp{R^2 + \beta^2/m}} + \frac{16}{\lambda} \exp\lrp{2\frac{7\aq\Rq^2}{3}}\lrp{L + \LN^2} \epsilon\\
=& 4\exp\lrp{\frac{7\aq\Rq^2}{3}}\lrp{e^{-\lambda i\delta} \lrp{R^2 + \beta^2/m}} + \hat{\epsilon}
\end{aligned}$$ By our assumption that $i\geq \frac{1}{\delta} \cdot 3\aq\Rq^2 \log \frac... | 1,070 | 648 | 1,014 | 1,032 | null | null | github_plus_top10pct_by_avg |
smooth.
Proof. We may assume that all occurring schemes are affine. Thus we have $I_i\subset R_i$ and $S_i\subset R_i/I_i$. Furthermore, $R_1$ is flat over $R_2$, $I_1=I_2R_1$ and $S_1$ is flat over $S_2$. We may also assume that $R_2$ is local. The key point is the isomorphism $$\bigl( R_1/I_1\bigr)\cong
\bigl( R_2/... | 1,071 | 1,886 | 1,416 | 1,025 | 1,493 | 0.788857 | github_plus_top10pct_by_avg |
n)^2}{(1-q^{n-1}t^{2n}T^n)(1-t^{2n+2}q^{n+1}
T^n)}
\label{GS}$$
with $H_c\left(X^{[n]};q,t\right):=\sum_{i,k}h_c^{i,i;k}(X^{[n]})q^it^k$.
Define $\H^{[n]}(z,w)$ such that $$H_c\left(X^{[n]};q,t\right)
=(t\sqrt{q})^{2n}\H^{[n]}\left(-t\sqrt{q},\frac{1}{\sqrt{q}}\right).$$ Then Formula (\[GS\]) reads $$\sum_{n\geq 0}... | 1,072 | 550 | 1,197 | 1,096 | null | null | github_plus_top10pct_by_avg |
ined in the second line of [(\[eq:diagbd-reorg\])]{}; let $Y_{m,l}$ be the supremum of what remains in the second line over $b_m,v_m,y_{l+1},v_{l+1}$. Then we can perform the sum of the first line over $b_m,v_m$ and the sum of the third line over $y_{l+1},v_{l+1}$ independently; the former is $O(\theta_0)^{m-1}$ and th... | 1,073 | 179 | 1,711 | 1,272 | 514 | 0.807383 | github_plus_top10pct_by_avg |
$m=h+(i-j)\geq h$ so that $a^mb^0\in S$. Hence $0\in I$.
Since $F_D\subseteq D\cap L_{min(I)}$, the following corollary is clear.
\[flo\]Let $S$ be a lower subsemigroup of $\mathcal{B}$. If $S$ is a left I-order in $\mathcal{B}$, then $F_D=\{1\}$ or $F_D=\emptyset$.
Suppose that a lower subsemigroup $S$ is a left I... | 1,074 | 1,397 | 1,243 | 1,172 | null | null | github_plus_top10pct_by_avg |
ypes.
Type 1. The points $\kappa(\bar x_1)$, $\kappa(\bar x_2)$ in $\RP^s$ are $\varepsilon_2$-close.
Type 2. The distances between the points $\kappa(\bar x_1)$, $\kappa(\bar x_2)$ in $\RP^s$ are greater then the caliber $\varepsilon_2$ of the regular approximation. Points of this type belong to the regular neighbor... | 1,075 | 1,541 | 1,107 | 1,047 | 3,901 | 0.769416 | github_plus_top10pct_by_avg |
nodes in a moded SLD-derivation such that all integer variables in $LHS$ are in $A_i^1$ and let $\underline{I_1},\ldots,\underline{I_n}$ be all integer variables of $A_i^1$.
If there exist subterms of $A_j^1$, $t_1,\ldots,t_n$, such that $\forall L: subterm(L,A_i^1)=\underline{I_p} \Longrightarrow
subterm(L,A_j^1)=t_... | 1,076 | 1,541 | 1,424 | 1,089 | 906 | 0.797953 | github_plus_top10pct_by_avg |
(\hat{\psi}_{{\widehat{S}}}).$$
This formulation of $\beta_{{\widehat{S}}}$ and $\hat{\beta}_{{\widehat{S}}}$ is convenient because, by expanding each coordinate of $g(\hat{\psi})$ separately through a first-order Taylor series expansion around $\psi$, it allows us to re-write $\hat{\beta}_{{\widehat{S}}} -
\beta_{{\w... | 1,077 | 963 | 1,433 | 1,196 | 2,333 | 0.780804 | github_plus_top10pct_by_avg |
$I^e$}},$$ $$(a_i, x_i^j, b_i, c_i, d_i, e_i, f_i)_{\textit{$L_i$ free of type $I$ with $i$ odd}}, (a_i, x_i^j, f_{i,i}^{\ast})_{\textit{$L_i$ bound of type $I$ with $i$ odd}})$$ of $\underline{H}(R)$ is denoted by $(f_{i,j}, a_i \cdots f_i)$.
\[r33\]
1. Recall that $\delta$ is a unit element in $A$ such that $\delt... | 1,078 | 3,763 | 1,217 | 793 | null | null | github_plus_top10pct_by_avg |
ght) + \left( {\theta + u_{2i}} \right)\textit{treat}_{\mathit{ij}} + e_{\mathit{ij}}} \\
& {\mspace{140mu} u_{1i} \sim N\left( {0,\tau_{\beta}^{2}} \right)} \\
& {\mspace{140mu} u_{2i} \sim N\left( {0,\tau^{2}} \right)} \\
& {\mspace{144mu} e_{\mathit{ij}} \sim N\left( {0,\sigma_{i}^{2}} \right)} \\
\end{matrix}$$ ... | 1,079 | 493 | 2,271 | 1,033 | 1,227 | 0.792386 | github_plus_top10pct_by_avg |
ptyset\})$ and ${\mathsf{Stab}_R}(\{\emptyset\})$ are the collection $\mathsf{POINT}$ of pointed derivators, while ${\mathsf{Abs}_L}(\mathsf{POINT})$ contains all cosieves and ${\mathsf{Abs}_R}(\mathsf{POINT})$ contains all sieves. In particular, $\mathsf{POINT}$ is a fixed point of both Galois correspondences. Similar... | 1,080 | 517 | 736 | 1,193 | 3,927 | 0.769239 | github_plus_top10pct_by_avg |
rms can be put together as before to produce a map $\chi_i$, so that now $\Upsilon_{i+1}:=\chi_2+\dots+\chi_i$ only maps into $M_{i+1}\oplus M_{i+2}\oplus\dots $. We therefore obtain the chain map $\chi$, and with this, we define the homotopy $\mathcal Comm$-inner product as $f:=\chi(\mu)\in Mod(F_{\mathcal Lie, C[1]}... | 1,081 | 674 | 1,522 | 1,130 | 744 | 0.800971 | github_plus_top10pct_by_avg |
_{-1/2}, spacetime vector, in chiral spinor of $so(16)$
\overline{\psi}^{1-2}_{-1/2} \right)$
------------------------------------------------------------------------------------------------------
Finally, let us consider the $k=3$ sector. There are no massless states in (R,NS), so we only consi... | 1,082 | 3,420 | 1,218 | 982 | null | null | github_plus_top10pct_by_avg |
form weights, and is generally inconsistent. However, when sample size is small, inconsistent estimators can achieve smaller variance leading to smaller error. Normalization constant $C$ is $10^{3}\ell/d^2$, and each point is averaged over $100$ trials. We use the minorization-maximization algorithm from [@Hun04] for c... | 1,083 | 475 | 233 | 1,018 | 717 | 0.801641 | github_plus_top10pct_by_avg |
sms of the third and the of forth t-maps has order two. Thus, they generate three tree-rooted cubic maps each and the second cubic map generates $18$ tree-rooted maps.
The third cubic map in Figure 1 generates three t-maps. $$\begin{picture}(270,95) \put(0,30){\circle*{3}} \put(70,30){\circle*{3}}
\put(35,50){\circle*... | 1,084 | 1,045 | 1,177 | 1,027 | null | null | github_plus_top10pct_by_avg |
the only semistandard tableaux which can occur in $\theta$ are those with a $2$ in each row, i.e. those of the form $$\young(1111233\star,2\star\star\star\star),\qquad
\young(111123\star\star,23\star\star\star)\quad\text{or}\quad
\young(11112\star\star\star,233\star\star).$$ Now the first and last of these three types... | 1,085 | 864 | 1,320 | 1,043 | 1,519 | 0.788653 | github_plus_top10pct_by_avg |
�\[pr:2\]]{} that $$\widehat{\alpha_{0}} = \{\alpha' | \, \alpha' (g, h) = r(g) h
r(g \lhd h)^{-1}, {\rm for ~ some ~} r: G\to {\rm Ker}(\beta) ~~
{\rm ~ a~ morphism~ of~ groups}\}$$
We record this observation in the following:
Let $H$, $G$ be two groups, $\beta: G \times H \rightarrow G$ an action as automorphisms a... | 1,086 | 2,081 | 1,275 | 1,051 | 3,847 | 0.769716 | github_plus_top10pct_by_avg |
f $C\le\lambda_0$, then $\lim_{t\to 0}{{\mathscr C}}\circ\alpha(t)$ is a $(0:1:0)$-star.
If $C=\frac ca\le\lambda_0$, then $f_{(C)}(y)=0$, so $$\alpha(t)=\begin{pmatrix}
1 & 0 & 0 \\
t^a & t^b & 0 \\
0 & 0 & t^c\end{pmatrix}\quad.$$ The statement follows by computing the limit of individual formal branches, using ... | 1,087 | 2,831 | 1,362 | 1,039 | 3,718 | 0.770521 | github_plus_top10pct_by_avg |
p (\mathbb{Z}_{k+1}^2 \times \mathbb{Z}_{6k} \times \{m\})$ are disjoint. Furthermore, if $C$ is the union of these two sets, then, for every $n$, $C \cap (\mathbb{Z}_{k+1}^2 \times \{n\} \times \{m\}) = \{a_r, \ldots, a_{r+k}\}$ for some $r$, and by Proposition \[anprop\], this contains either one point in every row o... | 1,088 | 719 | 1,066 | 1,146 | 1,520 | 0.788653 | github_plus_top10pct_by_avg |
n of elements of $\underline{M}(R)$ in Section \[m\]. Based on these, an element of $\tilde{M}(R)$ is $$m= \begin{pmatrix} \pi^{max\{0,j-i\}}m_{i,j} \end{pmatrix} \mathrm{~with~}z_i^{\ast}, m_{i,i}^{\ast}, m_{i,i}^{\ast\ast}$$ satisfying the following:
- If $i$ is even and $L_i$ is *of type* $\textit{I}^o$ (resp. *o... | 1,089 | 3,281 | 1,505 | 956 | 2,487 | 0.779375 | github_plus_top10pct_by_avg |
ber\,
4A_{\Sigma} K_{22} M_N i\left({\vec{\sigma}_1}\times
{\vec{\sigma}_2}\right){\vec{q}}\\-&\nonumber\,
4 A_{\Sigma} M_N\left({\vec{q}}^2 K_{23}+5 K_{34}+{\vec{q}}^2
K_{35}+K_{22}\right){\vec{\sigma}_1}\cdot {\vec{q}}\\+&\nonumber\,
2B_{\Sigma} K_{22} ({\vec{\sigma}_1}\cdot {\vec{q}})({\vec{\sigma}_2}\cdot {\... | 1,090 | 1,488 | 1,450 | 1,175 | null | null | github_plus_top10pct_by_avg |
now the Feynman–Kac representation of the solution to the above fractional Poisson problem, thanks to Theorem 3.2 in [@bucur] for domains which are balls, we are forced to conclude that $$\hat{u}(x) = \mathbb{E}_x\left[\hat{u} (X_{\sigma_{B(x')}}) + \int_0^{\sigma_{B(x')}} {f}(X_s)\,{\rm d}s\right], \qquad x\in B(x'),\... | 1,091 | 2,696 | 1,246 | 1,087 | null | null | github_plus_top10pct_by_avg |
\- \- **17%**
n individuals (NUTS II) 17,087 (99) 16,534 (99) 18,734 ... | 1,092 | 4,948 | 315 | 546 | null | null | github_plus_top10pct_by_avg |
with* *the filter* *$\mathcal{F}$, see Eq. (\[Eqn: DirectedNet2\]).$\qquad\square$*
**Definition A1.11.** *Let $\chi\!:\mathbb{D}\rightarrow X$ be a net and $\mathbb{R}_{\alpha}=\{\beta\in\mathbb{D}\!:\beta\succeq\alpha\in\mathbb{D}\}$ a residual in $\mathbb{D}$. Then* $$_{\textrm{F}}\mathcal{B}_{\chi}\overset{\textr... | 1,093 | 1,912 | 1,200 | 1,109 | 3,651 | 0.770915 | github_plus_top10pct_by_avg |
in {{\mathbb{Z}}}: M > N \Longrightarrow M+1>N$$ This implication is correct and thus proves non-termination for the considered queries if the precondition holds in the first iteration. This is the case for all queries in $Den(\leftarrow count\_to(\underline{N},L))$ with $0 > \underline{N}$ since the value correspondin... | 1,094 | 5,738 | 1,581 | 514 | 722 | 0.801514 | github_plus_top10pct_by_avg |
igned}
\lrabs{\psi'(r) \nu'r)}
=& \lrabs{\psi(r)(\aq \tau'(r)) \nu'r)}\\
\leq& \aq \lrabs{\tau'(r)}\lrabs{\psi(r) \nu'r)}\\
\leq& \frac{5\aq\Rq}{4} \cdot \frac{4}{\Rq}\\
\leq& 5\aq
\end{aligned}$$ Where the second last line follows form Lemma \[l:t... | 1,095 | 2,723 | 1,157 | 1,075 | null | null | github_plus_top10pct_by_avg |
lgebra, $$\begin{aligned}
[{\mathcal{S}}(\epsilon_1), {\mathcal{S}}(\epsilon_2)]\
=&\
\tilde{p}(v_{12})\,,
\label{1st quantized alg}\end{aligned}$$ with $v_{12}^\mu=(\epsilon_1C\bar{\gamma}^\mu\epsilon_2)/\sqrt{2}$, where $\tilde{p}(v)$ is the operator with picture number $p=-1$ defined by $$\tilde{p}(v)\ =\ v_\mu\ti... | 1,096 | 207 | 685 | 1,181 | null | null | github_plus_top10pct_by_avg |
\delta = \max_{j \in [n]} \bigg\{ 4 \delta_{j,1}^2 + \frac{2\big(\delta_{j,1}\delta_{j,2} +\delta_{j,2}^2\big)\kappa_j}{\eta_{j}\ell_j} \bigg\} \;\;\leq\;\; 28 (\log(\ell_{\max} +2))^2\,.\end{aligned}$$
Proof of Theorem \[thm:main\]
-----------------------------
We first introduce two key technical lemmas. In the fo... | 1,097 | 2,844 | 1,172 | 1,077 | null | null | github_plus_top10pct_by_avg |
e 1$ and that the claim holds for all smaller values of $m$. Let $j\in I$.
Suppose first that $j=i_m$. Then $$T_{i_1}\cdots T_{i_m}(E_j)= T_{i_1}\cdots T_{i_{m-1}}(F_{i_m}L_{i_m}^{-1})
=F_{\beta _m}L_{\beta _m}^{-1}.$$ Hence Eq. follows from Lemma \[le:rvrel\].
Suppose now that $j\not=i_m$. Let $\chi '=r_{i_{m-1}}... | 1,098 | 3,226 | 1,611 | 1,010 | null | null | github_plus_top10pct_by_avg |
26 23 S ribosomal RNA
1998333 A:6 C:495 C:185 6 13.8 ... | 1,099 | 4,870 | 302 | 626 | null | null | github_plus_top10pct_by_avg |
valuations use a simple Nelder-Mead algorithm to learn about the cost space. The machine learning algorithm (red and blue) optimizes to BEC faster than the Nelder-Mead (black). By utilizing the machine learning model a parameter is eliminated and the convergence improves (red).](figure3.pdf){width="\columnwidth"}
The ... | 1,100 | 683 | 2,237 | 1,150 | null | null | github_plus_top10pct_by_avg |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.